Nethack.alt.org
nethack.alt.org, commonly abbreviated to NAO, is one of the oldest NetHack public servers, and by far the most popular. To play, all you need is a Telnet client. On Windows, the built-in telnet.exe is adequate, though most prefer to use PuTTY. On Mac OS X and other UNIX-like systems, typing
telnet nethack.alt.org
at a command prompt will get you connected.
A wealth of information about the server, as well as detailed statistics, end-of-game dumps, tty recordings and the high score table is available on NAO's web site.
NAO is well integrated with #nethack on irc.freenode.net through the Rodney bot, which announces all deaths on the server, to the morbid delight of all.
nethack.alt.org runs vanilla NetHack with the following interface patches: menucolors, sortloot, chardump, showborn, hpmon, dgamelaunch mail.